Just how many individuals on death row are incorrectly convicted? The question has dogged attorneys and civil rights advocates for years, but a simple answer is almost impossible because few wrongful cases are ever overturned. A new analysis is adding a level of much-needed detail, and it concludes that more than twice as many inmates were wrongly convicted and sentenced to death than have been exonerated and freed.

Borrowing a statistical method often used to evaluate whether new medical therapies help patients survive, a team of researchers has concluded that about 4.1 percent of criminal defendants who are sentenced to death are falsely convicted. The approach allows researchers to “actually come up with a valid estimate of the rate of false convictions—knowing something that people say [in criminal justice] is not knowable,” says study author Samuel Gross, a law professor at the University of Michigan Law School and editor of the National Registry of Exonerations, a U.S.-focused exoneration database. What makes the analysis possible is that data on the potential need for exoneration from death penalty cases come to light more often than it does for other types of criminal proceedings. All death sentences in the U.S. are based on crimes that include homicide.

The study, led by a team of lawyers and statisticians, examined data on both 7,482 defendants who were given death sentences between 1973 and 2004 and death row exonerations during that time. By applying survival analysis—a statistical method often used to calculate how well new treatments help patients survive—they determined how often a prisoner under threat of execution was exonerated. The method usually tracks patients to see if a new therapy prolongs the period of time until a person dies from the illness in question but it can also be applied to policy questions that have clear end points. In this study the end point of tracking was exoneration (being found innocent and freed) or the actual execution. “Survival” was defined as remaining in prison. The “therapy” here would be removal of the threat of execution.

Here’s how their analysis works. It says that if all death-sentenced defendants remained under this sentence indefinitely, as opposed to being taken off death row due to being resentenced to life in prison or their fate being artificially cut off by the study ending, then 4.1 percent of those prisoners would have otherwise been exonerated. (And being exonerated and freed by legal action here is used as the best proxy for innocence.) The analysis also takes into account other occurrences such as suicide or death of a prisoner from natural causes. The number of false convictions among the death-sentenced has been particularly hard to estimate, Gross says, because many prisoners who are on death row are eventually moved off of it but remain in prison, which often reduces their chances of exoneration.

The issue affects a significant number of people. Since 1973 144 death-sentenced defendants have been exonerated in the U.S. But Gross says that the analysis indicates that at least 340 people would have been put to death unjustly in that same time period. “There are no other reliable estimates of the rate of false conviction in any context,” the researchers wrote in the study, published online on April 28 in Proceedings of the National Academy of Sciences.

The researchers also note that a 4.1 percent rate of false conviction is conservative, given that separate calculations gauging the accuracy of the assumptions that took an even more conservative stance—assuming that people who were executed had zero chance of false conviction and that the chances of exoneration after retrial would be twice that of people on death row—would still produce a larger figure than their 4.1 percent estimate. Although their analysis does not include data after 2004, the researchers note that they doubt that the use of DNA identification technology would have much impact on false conviction rates—because DNA evidence is primarily used in cases such as rape rather than homicide. Only about 13 percent of death row exonerations have resulted from DNA testing.

For more on death penalty considerations, see Scientific American’s editorial in the May edition of the magazine that details how the use of drugs to carry out capital punishment is inadvertently putting medical patients at risk.

Scientific American is part of Springer Nature, which owns or has commercial relations with thousands of scientific publications (many of them can be found at www.springernature.com/us). Scientific American maintains a strict policy of editorial independence in reporting developments in science to our readers.